We report on optically induced rotations of nematic liquid crystal droplets. We show experimentally that bipolar nematic liquid crystal droplets trapped in laser tweezers having circular polarization can exhibit nonlinear rotational motion, unlike optically trapped solid birefringent micro-plates. Such nonlinear rotations are retrieved by analyzing the polarization dynamics analysis of the light beam after it has passed through the droplet. The occurrence of complex dynamics is only found for large enough trapping power and droplet diameter. The analogy with optically induced nonlinear rotations in nematic liquid crystal films is briefly discussed.